Optimization-based Robot Compliance Control: Geometric and Linear Quadratic Approaches

Abstract

Impedance control is a compliance control strategy capable of accommodating both unconstrained and constrained motions. The performance of impedance controllers depends heavily upon environment dynamics and the choice of target impedance. To maintain performance for a wide range of environments, target impedance needs to be adjusted adaptively. In this paper, a geometric view on impedance control is developed for stiff environments, resulting in a "static-optimized" controller that minimizes a combined generalized position and force trajectory error metric. To incorporate the dynamic nature of the manipulator-environment system, a new cost function is considered. A classic quadratic optimal control strategy is employed to design a novel adaptive compliance controller with control parameters adjusted based upon environment stiffness and damping. In steady state, the proposed controller ultimately implements the static-optimized impedance controller. Simulation and experimental results indicate that the proposed optimal controller offers smoother transient response and a better trade-off between position and force regulation.

Exploiting Variable Stiffness in Explosive Movement Tasks

“…For example, the benefit of optimal time-varying stiffness control has been investigated in [9]. The utility of damping variation was shown in [6], where a robot hand controlled by an optimal variable damper effectively supported a human in a cooperative lifting task.…”

Continuous critic learning for robot control in physical human-robot interaction

“…This assumption makes the problem studied in this paper more complicated compared with previous study in [14].…”

“…Recalling (14) and (15), if the temporal difference (13) is used for the training of neural network with φ = z(t) ⊗ z(t), then we are able to approximate the existing quadratic cost function, i,e.,…”

Optimal Critic Learning for Robot Control in Time-Varying Environments

“…Remark 1: A e (k) and B e (k) are assumed to be unknown time-varying matrices in this paper. This assumption makes the problem studied in this paper more practical, yet more complicated compared with the previous studies in [8], [6].…”

“…Optimization is important in impedance learning/adaptation since its objective includes both the trajectory tracking and liy@i2r.a-star.edu.sg force regulation. In [7], [8], the well-known Linear Quadratic Regulator (LQR) optimal control is adopted for the proper selection of impedance parameters. Although mathematically elegant, this approach has a major drawback posed by the requirement that the environment dynamics are completely known.…”